if you play ruined rex. then target it with baited hook. it dies and you choose a target for its deathknell before you draw for baited hook correct? and in which case its on the chain. if your baited hook gives you karthus is that ruined rex 4 damage now doubled? does it double the chain item or double the amount of times it goes on chain?

Close, but two corrections — and the short answer is no, you don't get doubled damage.

You don't choose the Deathknell target before the draw. When Ruined Rex dies, its Deathknell trigger is created and added to the chain as a pending item right away (Rule 808.1.d.2), but it can't finalize — and targets are only chosen at finalization — until Baited Hook has fully finished resolving. So the target is picked after you look at the top 5 and play Karthus, and Karthus will already have entered before the trigger is placed on the chain.

Despite that, Karthus does not double it. His ability reads "Your [Deathknell] effects trigger an additional time," and it only applies if he's already on the battlefield at the moment the trigger is created. Here the trigger was created while Karthus was still in your deck, so you get one trigger and 4 damage, not 8.

On the last question: Karthus doubles the number of triggers (a second, separate chain item, resolved one at a time), not the damage value — so Ruined Rex would deal 4 twice, never 8 in one hit. This matches the established Baited Hook/Karthus line (FAQ #11068, #10051).